TSTP Solution File: GRP130-3.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:26:14 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 15:04:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(product_type, type, (
% 0.20/0.44 product: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(e_1_type, type, (
% 0.20/0.44 e_1: $i)).
% 0.20/0.44 tff(e_2_type, type, (
% 0.20/0.44 e_2: $i)).
% 0.20/0.44 tff(equalish_type, type, (
% 0.20/0.44 equalish: ( $i * $i ) > $o)).
% 0.20/0.44 tff(e_3_type, type, (
% 0.20/0.44 e_3: $i)).
% 0.20/0.44 tff(group_element_type, type, (
% 0.20/0.44 group_element: $i > $o)).
% 0.20/0.44 tff(cycle_type, type, (
% 0.20/0.44 cycle: ( $i * $i ) > $o)).
% 0.20/0.44 tff(e_0_type, type, (
% 0.20/0.44 e_0: $i)).
% 0.20/0.44 tff(greater_type, type, (
% 0.20/0.44 greater: ( $i * $i ) > $o)).
% 0.20/0.44 tff(next_type, type, (
% 0.20/0.44 next: ( $i * $i ) > $o)).
% 0.20/0.44 tff(1,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.44 tff(2,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.44 tff(8,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.44 tff(11,plain,(
% 0.20/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[10])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(14,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (~equalish(e_1, e_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[18, 16])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[21, 15, 12, 2, 1])).
% 0.20/0.45 tff(23,plain,((~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (~product(e_2, e_1, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[23, 1])).
% 0.20/0.45 tff(25,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.45 tff(26,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(28,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (~equalish(e_2, e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[32, 29, 12, 25, 26])).
% 0.20/0.45 tff(34,plain,((~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (~product(e_2, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[34, 25])).
% 0.20/0.45 tff(36,assumption,(product(e_1, e_1, e_3)), introduced(assumption)).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.45 tff(42,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.45 tff(45,plain,(
% 0.20/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[44])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 ((equalish(e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[52, 15, 46, 36, 25])).
% 0.20/0.45 tff(54,plain,((~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (~product(e_1, e_1, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[54, 25])).
% 0.20/0.45 tff(56,assumption,(~product(e_1, e_1, e_3)), introduced(assumption)).
% 0.20/0.45 tff(57,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)))), rewrite((((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.45 tff(63,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.45 tff(66,plain,(
% 0.20/0.45 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[65])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 ((product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1))) <=> ((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3))),
% 0.20/0.45 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[73, 67, 57, 56])).
% 0.20/0.46 tff(75,plain,((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (~product(e_3, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[75, 55])).
% 0.20/0.46 tff(77,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(79,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (~equalish(e_3, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 ((equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[86, 80, 46, 77, 25])).
% 0.20/0.46 tff(88,plain,((~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (~product(e_3, e_1, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[88, 25])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : refl(((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)))), rewrite((((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)))), rewrite((((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.46 tff(95,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.46 tff(98,plain,(
% 0.20/0.46 ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[97])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(101,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (group_element(e_3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(104,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 (group_element(e_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (((~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))) <=> (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[108, 106])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (product(e_3, e_1, e_1) | product(e_3, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[111, 105, 102, 99, 89])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (product(e_3, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 76])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 ((product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1))) <=> ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (~product(e_3, e_2, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[119, 67, 113, 35])).
% 0.20/0.47 tff(121,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.47 tff(122,assumption,(~product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 ((product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_2, e_2))) <=> (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[124])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[125, 123])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[128, 67, 122, 121])).
% 0.20/0.47 tff(130,plain,((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (~product(e_3, e_2, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[130, 35])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(133,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 (group_element(e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (((~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3))),
% 0.20/0.47 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (product(e_3, e_2, e_1) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[140, 134, 102, 99])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (product(e_3, e_2, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[141, 131, 120])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 ((product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_2))) <=> ((~product(e_3, e_1, e_2)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[145, 143])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[148, 67, 113, 89, 142])).
% 0.20/0.48 tff(150,plain,(~product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (((~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[152])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.20/0.48 inference(transitivity,[status(thm)],[153, 151])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (product(e_2, e_1, e_1) | product(e_2, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[156, 105, 134, 99, 150])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (product(e_2, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[157, 24])).
% 0.20/0.48 tff(159,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(160,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 ((product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2))) <=> (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[162])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[163, 161])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[166, 67, 160, 1, 159])).
% 0.20/0.48 tff(168,plain,((~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (product(e_1, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[168, 158, 1])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[172, 29, 46, 169, 158])).
% 0.20/0.48 tff(174,plain,(~product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(175,assumption,(~product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.48 tff(176,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 ((equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[178])).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[179, 177])).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[182, 80, 46, 176, 159])).
% 0.20/0.49 tff(184,plain,((~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (~product(e_3, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[184, 159])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 ((product(e_3, e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_2))) <=> (product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[187])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[188, 186])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 (product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[191, 67])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 (~product(e_2, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[192, 185, 159])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 (((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[195])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.49 inference(transitivity,[status(thm)],[196, 194])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(199,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[199, 134, 99])).
% 0.20/0.49 tff(201,plain,
% 0.20/0.49 (product(e_2, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[200, 193, 175])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(203,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.49 tff(205,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[204, 29, 12, 201, 159])).
% 0.20/0.49 tff(206,plain,((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(207,plain,
% 0.20/0.49 (~product(e_2, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[206, 174])).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 (product(e_2, e_1, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[157, 207])).
% 0.20/0.49 tff(209,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(210,plain,
% 0.20/0.49 ((product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(211,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[210])).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[211, 209])).
% 0.20/0.49 tff(213,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(214,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[214, 67, 160, 2])).
% 0.20/0.49 tff(216,plain,((~product(e_2, e_1, e_1)) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 (product(e_1, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[216, 208])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 (^[Y: $i, X: $i] : refl(((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[218])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(221,plain,
% 0.20/0.49 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[221])).
% 0.20/0.49 tff(223,axiom,(![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle6')).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.20/0.49 tff(226,plain,(
% 0.20/0.49 ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[225])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[226, 219])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 (greater(e_2, e_1) <=> greater(e_2, e_1)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(229,axiom,(greater(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_greater_e_1')).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (greater(e_2, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 (((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[232])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[233, 231])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_2))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[236, 230, 227])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 (~cycle(e_1, e_0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[237, 217])).
% 0.20/0.49 tff(239,assumption,(cycle(e_2, e_0)), introduced(assumption)).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[240])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) <=> ((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> (((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))))), rewrite((((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> (((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))))), rewrite((((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> (((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))))), rewrite((((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(244,plain,
% 0.20/0.50 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[243])).
% 0.20/0.50 tff(245,axiom,(![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle5')).
% 0.20/0.50 tff(246,plain,
% 0.20/0.50 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.50 tff(247,plain,
% 0.20/0.50 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.20/0.50 tff(248,plain,(
% 0.20/0.50 ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[247])).
% 0.20/0.50 tff(249,plain,
% 0.20/0.50 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.20/0.50 tff(250,plain,
% 0.20/0.50 (cycle(e_3, e_0) <=> cycle(e_3, e_0)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(251,axiom,(cycle(e_3, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle3')).
% 0.20/0.50 tff(252,plain,
% 0.20/0.50 (cycle(e_3, e_0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.50 tff(253,plain,
% 0.20/0.50 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(254,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.20/0.50 tff(255,plain,
% 0.20/0.50 (greater(e_1, e_0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.20/0.50 tff(256,plain,
% 0.20/0.50 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(257,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.20/0.50 tff(258,plain,
% 0.20/0.50 (next(e_2, e_3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.20/0.50 tff(259,plain,
% 0.20/0.50 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(260,plain,
% 0.20/0.50 (((~greater(e_1, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_1))) <=> ((~cycle(e_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(261,plain,
% 0.20/0.50 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[260])).
% 0.20/0.50 tff(262,plain,
% 0.20/0.50 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[261, 259])).
% 0.20/0.50 tff(263,plain,
% 0.20/0.50 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(264,plain,
% 0.20/0.50 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.20/0.50 tff(265,plain,
% 0.20/0.50 ((~cycle(e_2, e_0)) | (~cycle(e_1, e_1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[264, 258, 255, 230, 252, 249])).
% 0.20/0.50 tff(266,plain,
% 0.20/0.50 (~cycle(e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[265, 239])).
% 0.20/0.50 tff(267,plain,
% 0.20/0.50 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(268,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.20/0.50 tff(269,plain,
% 0.20/0.50 (greater(e_2, e_0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.20/0.50 tff(270,plain,
% 0.20/0.50 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(271,plain,
% 0.20/0.50 (((~greater(e_2, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2))) <=> ((~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(272,plain,
% 0.20/0.50 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[271])).
% 0.20/0.50 tff(273,plain,
% 0.20/0.50 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[272, 270])).
% 0.20/0.50 tff(274,plain,
% 0.20/0.50 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(275,plain,
% 0.20/0.50 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.20/0.50 tff(276,plain,
% 0.20/0.50 ((~cycle(e_2, e_0)) | (~cycle(e_1, e_2))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[275, 258, 269, 230, 252, 249])).
% 0.20/0.50 tff(277,plain,
% 0.20/0.50 (~cycle(e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[276, 239])).
% 0.20/0.50 tff(278,plain,
% 0.20/0.50 (^[X: $i] : refl((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(279,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[278])).
% 0.20/0.50 tff(280,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(281,plain,
% 0.20/0.50 (^[X: $i] : trans(monotonicity(rewrite((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) <=> (cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> ((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)))), rewrite(((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(282,plain,
% 0.20/0.50 (![X: $i] : ((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> ![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[281])).
% 0.20/0.50 tff(283,axiom,(![X: $i] : ((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle2')).
% 0.20/0.50 tff(284,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.20/0.50 tff(285,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.20/0.50 tff(286,plain,(
% 0.20/0.50 ![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[285])).
% 0.20/0.50 tff(287,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[286, 279])).
% 0.20/0.50 tff(288,plain,
% 0.20/0.50 (((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))) <=> ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(289,plain,
% 0.20/0.50 ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(290,plain,
% 0.20/0.50 ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.20/0.50 tff(291,plain,
% 0.20/0.50 (cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[290, 287, 105])).
% 0.20/0.50 tff(292,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[291, 277, 266, 238])).
% 0.20/0.50 tff(293,plain,(~cycle(e_2, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(294,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.20/0.50 tff(295,plain,
% 0.20/0.50 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : refl(((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(296,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[295])).
% 0.20/0.50 tff(297,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(298,plain,
% 0.20/0.50 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) <=> ((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> (((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))))), rewrite((((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> (((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))))), rewrite((((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> (((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)))), rewrite((((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(299,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[298])).
% 0.20/0.50 tff(300,axiom,(![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle4')).
% 0.20/0.50 tff(301,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.20/0.50 tff(302,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.20/0.50 tff(303,plain,(
% 0.20/0.50 ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[302])).
% 0.20/0.50 tff(304,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[303, 296])).
% 0.20/0.50 tff(305,plain,
% 0.20/0.50 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(306,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.20/0.50 tff(307,plain,
% 0.20/0.50 (next(e_0, e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.20/0.50 tff(308,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(309,plain,
% 0.20/0.50 (((~cycle(e_2, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(310,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[309])).
% 0.20/0.51 tff(311,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[310, 308])).
% 0.20/0.51 tff(312,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(313,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.20/0.51 tff(314,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[313, 307, 258, 269, 252, 304, 29, 294])).
% 0.20/0.51 tff(315,plain,(~cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(316,plain,
% 0.20/0.51 (((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))) <=> ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(317,plain,
% 0.20/0.51 ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(318,plain,
% 0.20/0.51 ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.20/0.51 tff(319,plain,
% 0.20/0.51 (cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[318, 287, 134])).
% 0.20/0.51 tff(320,plain,
% 0.20/0.51 (cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[319, 315])).
% 0.20/0.51 tff(321,plain,
% 0.20/0.51 (cycle(e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[320, 293])).
% 0.20/0.51 tff(322,plain,
% 0.20/0.51 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(323,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.51 tff(324,plain,
% 0.20/0.51 (~equalish(e_1, e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.20/0.51 tff(325,plain,
% 0.20/0.51 (^[Z: $i, Y: $i, X: $i, X1: $i] : refl(((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(326,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[325])).
% 0.20/0.51 tff(327,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(328,plain,
% 0.20/0.51 (^[Z: $i, Y: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(329,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[328])).
% 0.20/0.51 tff(330,axiom,(![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle7')).
% 0.20/0.51 tff(331,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.20/0.51 tff(332,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[331, 327])).
% 0.20/0.51 tff(333,plain,(
% 0.20/0.51 ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[332])).
% 0.20/0.51 tff(334,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[333, 326])).
% 0.20/0.51 tff(335,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(336,plain,
% 0.20/0.51 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(337,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[336])).
% 0.20/0.51 tff(338,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[337, 335])).
% 0.20/0.51 tff(339,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(340,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.20/0.51 tff(341,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[340, 258, 255, 334, 324, 321, 208])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------